Solving problems

My friend is having difficulty in a question. She showed me and I can't quite nut it out now I've gone curious and would like to no the answer and how you do it.

The Question is:

A manufacturer sells a particular prodcut for $40 per unit. The manufacturer's costs for prodcuing the units consist of a fixed $5000 plus a cost of $22 per unit. If the manufacturer produces and sells x units find

a) The value of the x for the manufacturer to at least 'break even'. (Aussume that x must take interger values)

My friend is having difficulty in a question. She showed me and I can't quite nut it out now I've gone curious and would like to no the answer and how you do it.

The Question is:

A manufacturer sells a particular prodcut for $40 per unit. The manufacturer's costs for prodcuing the units consist of a fixed $5000 plus a cost of $22 per unit. If the manufacturer produces and sells x units find

a) The value of the x for the manufacturer to at least 'break even'. (Aussume that x must take interger values)

Thank you.

At break even revenue=costs.

R=40x

C=5000+22x

hence for break even:

40x=5000+22x

Now solve for x, if this is not an integer then you will need the next larger integer.